Algebra 2 Common Core

Published by Prentice Hall
ISBN 10: 0133186024
ISBN 13: 978-0-13318-602-4

Chapter 14 - Trigonometric Identities and Equations - 14-1 Trigonometric Identities - Practice and Problem-Solving Exercises: 34

Answer

$$\tan\theta$$

Work Step by Step

Simplify $$\sin^{2}\theta\csc\theta\sec\theta.$$ Use the Reciprocal Identities $$\csc\theta=\frac{1}{\sin\theta}$$ and $$\sec\theta=\frac{1}{\cos\theta}$$ to obtain $$\sin^{2}\theta\csc\theta\sec\theta=\sin^{2}\theta\bigg(\frac{1}{\sin\theta}\bigg)\bigg(\frac{1}{\cos\theta}\bigg)=\frac{\sin\theta}{\cos\theta}=\tan\theta,$$ with the last equality based on the Tangent Identity.
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